UCLA

A prominent goal within the field of modern heavy-ion collisions is to uncover the phase diagram of QCD. Studies of the properties of systems created in heavy-ion collisions strongly suggest that a new state of matter described by quark and gluon degrees of freedom, the quark-gluon plasma, is created when nuclei are collided at very high-energies. Consequently, the QCD phase diagram may contain a rich structure in regions currently accessible to heavy-ion experiments, including a possible critical point where the transformation between hadronic and partonic matter changes from a smooth crossover to a first-order phase transition. Whether this is the case will have to be born out through a combination of experimental analyses and state-of-the-art simulations of heavy-ion collisions.

We present a mean-field model of the dense nuclear matter equation of state designed for use in computationally demanding hadronic transport simulations. Our approach, based on the relativistic Landau Fermi-liquid theory, allows us to construct a family of equations of state spanning a wide range of possible bulk properties of dense QCD matter. For the application to simulations of heavy-ion collisions at intermediate beam energies, and in particular having in mind studies centered on probing the regions of the QCD phase diagram most relevant to the search for the QCD critical point, we further present and discuss parametrizations of the developed equation of state describing dense nuclear matter with two phase transitions: the known nuclear-liquid gas phase transition in ordinary nuclear matter, with its experimentally observed properties, and a postulated phase transition at high temperatures and high baryon number densities, meant to model the QCD phase transition from hadronic to quark and gluon degrees of freedom.

We implement the developed model in the hadronic transport code SMASH, and show that the resulting dynamic behavior reproduces theoretical expectations for the thermodynamic properties of the system based on the underlying equation of state. In particular, we discuss simulations of systems initialized in regions of the phase diagram affected by the conjectured QCD critical point, and we demonstrate that they reproduce effects due to critical behavior. Specifically, we show that pair distribution functions calculated from hadronic transport simulation data are consistent with theoretical expectations based on the second-order cumulant ratio, and can be used as a signature of crossing the phase diagram in the vicinity of a critical point. Through this, we validate the use of hadronic transport codes as a tool to study signals of a phase transition in dense nuclear matter.

We additionally present a novel method that may enable a measurement of the speed of sound and its derivative with respect to the baryon number density in heavy-ion collisions. The devised approach is based on a connection between the speed of sound and the cumulants of the net baryon number, which in the context of the search for the QCD critical point are given considerable attention due to their potential to signal critical fluctuations. We confirm the applicability of the proposed method in two models of dense nuclear matter, including the parametrization of the equation of state developed in this work. Application of our approach to available experimental data implies that the derivative of the speed of sound is non-monotonic in systems created in collisions at intermediate to low energies, which in turn may be connected to non-trivial features in the underlying equation of state.